Multi-chimera states in a higher order network of FitzHugh–Nagumo oscillators

Multi-chimera states in a higher order network of FitzHugh–Nagumo oscillators

14 March 2024 | Zhen Wang, Mingshu Chen, Xiaoqian Xi, Huaigu Tian, and Rui Yang
This study investigates the emergence of multi-chimera states in a higher-order network of FitzHugh–Nagumo (FHN) oscillators. A multi-chimera state is characterized by the coexistence of multiple synchronized and asynchronous groups. The research explores how higher-order interactions influence the occurrence and characteristics of multi-chimera states. The study uses measures of incoherence and discontinuity to analyze the network dynamics. Results show that higher-order networks are more likely to exhibit multi-chimera states. Additionally, lower first-order coupling strength can lead to complete coherence. The higher-order network also exhibits imperfect chimera and imperfect synchronization. The network model consists of coupled identical FHN systems with non-local coupling. The model includes both first-order and second-order interactions. The first-order coupling strength is denoted by σ, while the second-order coupling strength is denoted by σ₂. The study also introduces a statistical measure called the strength of incoherence (SI) to detect chimera states. The SI is calculated based on the difference between the average of the oscillators' phases and the average of their frequencies. The results show that the region of occurrence of multi-chimera states increases in higher-order networks. The study also finds that the regions of multi-chimera states change with the inclusion of higher-order interactions. The findings suggest that higher-order interactions can significantly influence the collective behavior of oscillatory networks. The study provides insights into the complex dynamics of multi-chimera states in higher-order networks of FHN oscillators.This study investigates the emergence of multi-chimera states in a higher-order network of FitzHugh–Nagumo (FHN) oscillators. A multi-chimera state is characterized by the coexistence of multiple synchronized and asynchronous groups. The research explores how higher-order interactions influence the occurrence and characteristics of multi-chimera states. The study uses measures of incoherence and discontinuity to analyze the network dynamics. Results show that higher-order networks are more likely to exhibit multi-chimera states. Additionally, lower first-order coupling strength can lead to complete coherence. The higher-order network also exhibits imperfect chimera and imperfect synchronization. The network model consists of coupled identical FHN systems with non-local coupling. The model includes both first-order and second-order interactions. The first-order coupling strength is denoted by σ, while the second-order coupling strength is denoted by σ₂. The study also introduces a statistical measure called the strength of incoherence (SI) to detect chimera states. The SI is calculated based on the difference between the average of the oscillators' phases and the average of their frequencies. The results show that the region of occurrence of multi-chimera states increases in higher-order networks. The study also finds that the regions of multi-chimera states change with the inclusion of higher-order interactions. The findings suggest that higher-order interactions can significantly influence the collective behavior of oscillatory networks. The study provides insights into the complex dynamics of multi-chimera states in higher-order networks of FHN oscillators.
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